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#362×C₁₃₉ #22580447

order	8896
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂

Aliases

#362×C₁₃₉

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃₉	#102
commutator	C₈	C₂×C₄×C₁₃₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₉
prime radical	C₂²×C₁₃₉	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₉ ◁ C₂×C₄×C₁₃₉ ◁ C₂×C₈×C₁₃₉ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2224 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#362×D₁₃₉, #31808152, #31808298, …
maximal subgroup of	C₂×#362×C₁₃₉, #2148×C₁₃₉, #2180×C₁₃₉, …
maximal normal subgroup of	C₂×#362×C₁₃₉, #2148×C₁₃₉, #2180×C₁₃₉, …
maximal quotient of	#1334×C₁₃₉, #1350×C₁₃₉, #1362×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 43);